The least weakly compact cardinal can be unfoldable, weakly measurable and nearly θ-supercompact

2013/05/25 by Brent Cody, Moti Gitik, Cody, Brent +5
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.1305.5961

openalex publication_date 2013/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove from suitable large cardinal hypotheses that the least weakly compact cardinal can be unfoldable, weakly measurable and even nearly θ-supercompact, for any desired θ. In addition, we prove several global results showing how the entire class of weakly compact cardinals, a proper class, can be made to coincide with the class of unfoldable cardinals, with the class of weakly measurable cardinals or with the class of nearly θ_κ-supercompact cardinals κ, for nearly any desired function κ↦θ_κ. These results answer several questions that had been open in the literature and extend to these large cardinals the identity-crises phenomenon, first identified by Magidor with the strongly compact cardinals.

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